Multidimensional semicircular limits on the free Wigner chaos
Probability
2011-07-27 v1 Operator Algebras
Abstract
We show that, for sequences of vectors of multiple Wigner integrals with respect to a free Brownian motion, componentwise convergence to semicircular is equivalent to joint convergence. This result extends to the free probability setting some findings by Peccati and Tudor (2005), and represents a multidimensional counterpart of a limit theorem inside the free Wigner chaos established by Kemp, Nourdin, Peccati and Speicher (2011).
Keywords
Cite
@article{arxiv.1107.5135,
title = {Multidimensional semicircular limits on the free Wigner chaos},
author = {Ivan Nourdin and Giovanni Peccati and Roland Speicher},
journal= {arXiv preprint arXiv:1107.5135},
year = {2011}
}
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11 pages